Tensor Calculus Made Simple

by Taha Sochi

This book is about tensor analysis. It consists of 169 pages. The language and method used in presenting the ideas and techniques of tensors make it very suitable as a textbook or as a reference for an introductory course on tensor algebra and calculus or as a guide for self-studying and learning. The book contains many exercises. The detailed solutions of all these exercises are available in another book by the author (Solutions of Exercises of Tensor Calculus Made Simple).

Genres: Mathematics

170 pages, Kindle Edition

Published February 1, 2017

Reviews

[Andrew Davis · Rating 3 out of 5]

This book assumes only standard undergraduate calculus and linear algebra. It is intended to be a bridge between elementary vector calculus and more advance treatments. It is quite compact (about 120 pages without exercises) but systematic, progressing from basic linear algebra ideas to the geometry of curved spaces. Having introduced tensors and their algebra it continues with different coordinate systems and their transformations, before introducing the metric tensor, covariant differentiation and finally describing curvature and the Riemann tensor. A brief description of tensors application in mechanics, electromagnetism and general relativity concludes the book.

At the end of each chapter one finds a large number of exercises. Unfortunately, a separate book is required to check their solutions. Another problem is an absence of any sample exercises within the text itself. This would enhance the overall understanding. Only three stars from me.

[John Thompson · Rating 3 out of 5]

Terse, Not Simple

The book is quite terse and is often not that simple. There are too few examples. Definitions are given but seldom well motivated. There are exercises but you need a different book to verify your answers. Footnotes are held to a final chapter outside of their context. I frequently found myself needing to consult outside material. The focus was too much on the notation rather than on meaning or utility. I like brevity, but not at the expense of clarity and understanding. (For reference, I took linear algebra, vector analysis, differential equations, and other classes in university several years ago, but not any courses covering tensors.)

The book looked nice on my kindle. It was very legible. I liked the explanations of the coordinate systems and their diagrams. I learned new things about, for example, the permutation tensors and other topics. But, the book could have been more helpful.

Topics that could be explained or motivated better include covariance, contravariance, Chrostoffel symbols, the metric tensor, and more.

[Stephen · Rating 4 out of 5]

A good book on a difficult but necessary subject. This one was along the lines of a Schaum's outline book, with plenty of problems, but better. Taha explained the material very well so if you want to brush up on tensor calculus or learn it for the first time through self teaching, this book may just do the trick. Just note that this book will take effort on your part especially since you'll have to do the problems. As Taha says, the problems at the end of each chapter are not for decorative purposes.

[Richard Chamberlain · Rating 5 out of 5]

A tech book I would highly recommend to those with interest inMath

A really concise review for undergrad engineering and Physic disciplines, as pertaining to Vector and Tensor math. It also is a nice prep for understanding of the Tensor Math required for Einstein's theory of General Relativity.

[Alex Smith · Rating 4 out of 5]

Very good introduction to tensor calculus.